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A181293 Triangle read by rows: T(n,k) is the number of 2-compositions of n having k 0's (0<=k<=n) A 2-composition of n is a nonnegative matrix with two rows, such that each column has at least one nonzero entry and whose entries sum up to n. 1
1, 0, 2, 1, 2, 4, 2, 6, 8, 8, 4, 14, 24, 24, 16, 8, 32, 64, 80, 64, 32, 16, 72, 164, 240, 240, 160, 64, 32, 160, 408, 680, 800, 672, 384, 128, 64, 352, 992, 1848, 2480, 2464, 1792, 896, 256, 128, 768, 2368, 4864, 7296, 8288, 7168, 4608, 2048, 512, 256, 1664, 5568 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The sum of entries in row n is A003480(n).

Sum_{k=0..n} k*T(n,k) = A181294(n).

LINKS

Table of n, a(n) for n=0..57.

G. Castiglione, A. Frosini, E. Munarini, A. Restivo and S. Rinaldi, Combinatorial aspects of L-convex polyominoes, European J. Combin. 28 (2007), no. 6, 1724-1741.

FORMULA

G.f.: G(t,z) = (1-z)^2/(1-2*z-2*t*z+2*t*z^2).

G.f. of column k is 2^k*z^k*(1-z)^{k+2}/(1-2*z)^{k+1} (we have a Riordan array).

EXAMPLE

T(2,0)=1, T(2,1)=2, T(2,2)=4 because the 2-compositions of 2, written as (top row/bottom row), are (1/1), (0/2), (2/0), (1,0/0,1), (0,1/1,0), (1,1/0,0), (0,0/1,1).

Triangle starts:

1;

0,2;

1,2,4;

2,6,8,8;

4,14,24,24,16;

...

MAPLE

G := (1-z)^2/(1-2*z-2*t*z+2*t*z^2): Gser := simplify(series(G, z = 0, 14)): for n from 0 to 10 do P[n] := sort(coeff(Gser, z, n)) end do: for n from 0 to 10 do seq(coeff(P[n], t, k), k = 0 .. n) end do; # yields sequence in triangular form

CROSSREFS

Cf. A003480, A181294.

Sequence in context: A329688 A217920 A137406 * A262876 A263045 A333442

Adjacent sequences:  A181290 A181291 A181292 * A181294 A181295 A181296

KEYWORD

nonn,tabl

AUTHOR

Emeric Deutsch, Oct 12 2010

STATUS

approved

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Last modified September 23 19:43 EDT 2021. Contains 347617 sequences. (Running on oeis4.)